Another circuit problem for you?

Question

A silver wire (density = 10.50 g/cm^3) has a mass of 4.600 kg and a total resistance of 3.450 ohms. Determine the total length of the wire.

Answer 1

lets calculate the volume first:
V= M/d = 4600/10.5 = 438.095cm3 =438.095X10^(-6) m3=AXl
A= area of crossection
l=length of wire
A=V/l
Resistivity of Silver is 1.59 × 10-8 Ωm (0.0000000159 Ωm).=rho
R=rho l/A
R=1.59 × 10-8 X l^2/438.095X10^(-6) = 3.45
l^2=95058.35
l=308.315m

Answer 2

Volume = Mass / Density = 4600 / 10.5 = 438.1 cc

If r is the radius of the wire, pi.r^2 will be the area of the cross-section. If L is the length of the wire, resistance will be

R = k.L/ A where k is the specific resistance, L is the length in meters and A the area of cross-section in sq.meters. k is given in Ohm.m and for silver the value is 1.59 x 10^-8

3.45 = 1.59 x 10^-8 L / A

Volume = 438.1cc = 438.1/10^-6 cubic meters. = A x L

A = V/L = 438.1/L10^-6 meters

Substituting that in the other equation for resistance, we can write,

3.45 = 1.59 x 10^-8 L/ 438.1/L10^-6

3.45 = 1.59 x 10^-8 x L^2 x 10^-6/438.1 (a/b/c is ac/b)

L^2 = 3.45 x 438.1 / (1.59 x 10^-14)

L^2 = 950.6 x 10^14

L = 30.83 x 10^7 m

Answer 3

The resistance-resistivity relation can help.
R = resistance;
r = resistivity;
L = length;
A = cross sectional area;

Use the following formula :-
R = r*L/A --- --- --- --- ------ --- --- --- (1);
See a handbook to find 'r' for silver.
R = 3.45 ohms (given);
So, L/A can be found out from fromula (1).

Volume 'V' can be found out from the following formula as mass of the wire and its density are given:-
V = M/d --- --- --- --- --- --- --- --- (2);
(where M = mass, and, d = density).

V= L*A --- --- --- --- --- --- --- --- --- (3);

Knowing L/A from (1) and L*A from (3), you can easily find the value of 'L' or length.